An octagonal number is a number that is represented by the set of figures given below.

A certain octagonal number is the sum of the squares of three terms in an arithmetic sequence with a common difference of 704. What is that octagonal number?

I looked around, and the formula for the n-th octogonal number is 3n²-2n.

Three terms in arithmetic sequence can be m-704, m, m+704. (Writing them this way helps, because certain terms will be cancelled out.) The sum of their squares is 3m²+2.704².

Now, you only (!) have to solve 3n²-2n= 3m²+2.704² for integer m, n...

Posted by e.g. on 2006-06-13 09:56:52